423 articles – 192 references  [version française]

hal-00675045, version 3

## Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring

Sorina Ionica () 1

• 1:  CARAMEL (INRIA Nancy - Grand Est / LORIA)

• INRIA – CNRS : UMR7503 – Université de Lorraine France
• Available versions :  v1 (2012-02-29) v2 (2012-03-29) v3 (2012-04-20) v4 (2013-05-02)
• ### Bibliographic reference

• Type of document: Documents without publication reference (Preprint)
• Subject: Mathematics/General Mathematics
• Title: Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring
• Abstract: Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the $\ell$-Tate pairing in terms of the action of the Frobenius on the $\ell$-torsion of the Jacobian of a genus 2 curve. We apply similar techniques to study the non-degeneracy of the $\ell$-Tate pairing restrained to subgroups of the $\ell$-torsion which are maximal isotropic with respect to the Weil pairing. First, we deduce a criterion to verify whether the jacobian of a genus 2 curve has maximal endomorphism ring. Secondly, we derive a method to construct horizontal $(\ell,\ell)$-isogenies starting from a jacobian with maximal endomorphism ring.
• Fulltext language: English
• Keyword(s): abelian variety – Tate pairing – Galois cohomology
• ANR Project:  Project Id ANR CHIC Year 2009 Project acronyme CHIC Project title Courbes Hyperelliptiques, Isognénies, Comptage

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• hal-00675045, version 3
• oai:hal.archives-ouvertes.fr:hal-00675045
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• Submitted on: Friday, 20 April 2012 18:15:54
• Updated on: Friday, 20 April 2012 21:55:23